Serious interval estimation problem

Q.
The electro-motive force (emf) of batteries produced by a company is normally distributed with mean and variance of 45.1 and 0.0016 respectively .
If 4 such batteries are connected in series ,find the 50% confidence interval of the mean emf .How do you explain the results to a non-statistician ??

We are already given the mean and the variance of the population .
So here what is meant by 50% confidence interval ?

A 50 percent confidence interval is lame.
That means that the coverage isn't very good.
It says that in the long run (law of large numbers)
half of your intervals will contain the mean and half won't.
Not a desireable result at all.

A 50 percent confidence interval is lame.
That means that the coverage isn't very good.
It says that in the long run (law of large numbers)
half of your intervals will contain the mean and half won't.
Not a desireable result at all.

I could not understand about what you are talking .
Why are we searching for a 50% confidence interval here since we know the population parameter ?

The only thing I can think of, but that involves repeated confidence interval estimation is an exercise I did out of wackerly's book.
I made my students generate 100 uniforms on excel, then transform then to exponentials with a set mean. WE knew the mean.
Then they obtained a 95 percent CI for that known mean.
I made them do that 100 times, so there were 100 times 100= 10,000 observations.
Approximately 95 percent of these intervals contained that mean.
Some students had 93, others had 96 of them containing the mean.
That's the only thing I can think of.
They can see if the interval truly contains the mean.

sure, but you need normality
it would be a t density with 3 degrees of freedom, thats with s.
and you should do it over and over again.
HOWEVER if you know sigma, it's a normal rv.
It's the (strong) law of large numbers.

please

Originally Posted by matheagle

The only thing I can think of, but that involves repeated confidence interval estimation is an exercise I did out of wackerly's book.
I made my students generate 100 uniforms on excel, then transform then to exponentials with a set mean. WE knew the mean.
Then they obtained a 95 percent CI for that known mean.
I made them do that 100 times, so there were 100 times 100= 10,000 observations.
Approximately 95 percent of these intervals contained that mean.
Some students had 93, others had 96 of them containing the mean.
That's the only thing I can think of.
They can see if the interval truly contains the mean.

Originally Posted by matheagle

sure, but you need normality
it would be a t density with 3 degrees of freedom, thats with s.
and you should do it over and over again.
HOWEVER if you know sigma, it's a normal rv.
It's the (strong) law of large numbers.

that is what I did first ,but the problem came after solving the question
Can you please show me the steps of repeating the process ?